A Computational Introduction to Number Theory and Algebra (2nd Edition)
by Victor Shoup · Cambridge University Press
Covers congruences, distribution of primes, quadratic reciprocity, groups, rings, fields, and discrete probability, together with the algorithms and complexity analysis that public-key cryptography depends on. Published by Cambridge; the author hosts the complete PDF at no cost.
More resources on Cryptography Math
Elliptic Curves: Number Theory and Cryptography (2nd Edition)
Reference on elliptic curves over finite fields: the group law, torsion points, endomorphisms, Weil and Tate-Lichtenbaum pairings, point counting, and the discrete logarithm attacks that determine ECC key sizes. Covers projective, Jacobian, and Edwards coordinates.
A Graduate Course in Applied Cryptography
Graduate treatment of provable security: definitions, reductions, and proofs for ciphers, message authentication, public-key encryption, elliptic curves, lattices, zero-knowledge proofs, and multiparty computation. Appendices develop the number theory and probability used throughout. Complete PDF free from the authors.
An Introduction to Mathematical Cryptography (2nd Edition)
Undergraduate textbook developing the number theory, abstract algebra, and probability behind RSA, Diffie-Hellman, elliptic curve cryptography, lattice schemes, and digital signatures. Each chapter builds the required mathematics first, then the cryptosystem, with worked examples and exercises.